Pricing Methodology

Derivation of prices within the GRVT protocol.

The GRVT Docs are a living document that will be dynamically and continuously edited and updated as the GRVT product suite evolves.

Overview

Oracle data feeds provided by Block Scholes are completely and verifiably trustless, through the use of EIP712 cryptographic signatures. This means GRVT smart contracts can always ensure the data has not been tampered with, and is genuinely as attested by Block Scholes as a regulated & independent 3rd party provider.

GRVT offers the following prices via our Market Data endpoint.

  • Mark Price

    • Mark price is the fair, and authoritative price of a derivative contract on GRVT.

    • GRVT uses it to compute margin requirements, vault balance, and liquidation eligibility.

    • It is supplied by a third-party oracle to ensure that GRVT has no way to manipulate mark prices.

    • As GRVT is a hybrid exchange (HEX), mark prices are trustless similar to other DEXes.

  • Index Price

    • Index price is the aggregate derivative contract price sourced from leading CEXes.

    • GRVT uses it as a reference price to trigger temporary trading halts on our order book.

  • Mid Price

    • Mid Price is the average of the best bid and best ask prices on our order book.

    • GRVT uses it to adjust GRVT’s mark price closer to pre-trade prices on our exchange.

    • When it diverges too far from the index price, GRVT triggers a trading halt on our order book.

  • Last Price

    • Last Price is the last transacted price of a derivative contract on GRVT.

    • GRVT uses it to adjust GRVT’s mark price closer to post-trade prices on our exchange.

  • Settlement Price

    • All standard options and futures on GRVT are settled at 8am UTC on the expiration date.

    • The settlement price will leverage a highly precise spot index price.

Both Mid Price and Last Price are fairly trivial and standardised concepts, so this document will not go into deeper detail about these prices.

Price Sources

These are the price sources used to compute GRVT’s Index Price and Mark Price.

Spot/Futures/Perps (TBC)

  • Binance

  • OKX

  • Bybit

  • Deribit

Options

  • Deribit

  • OKX

  • Bybit

Index Price

The index_price for all derivatives is simply the VWAP of mid_prices retrieved from our source exchanges.

All index prices are delivered at 200ms frequency on our Market Data endpoints.

Settlement Price

index_price and settlement_price are highly similar. They both leverage VWAP of mid_prices. The only difference is:

  • index_price trades away accuracy for responsiveness.

    • index_prices are always published at the 200ms mark.

    • It will perform a VWAP over the latest mid_prices obtained from each exchange.

    • If an exchange is late to publish its price, index_price will not wait for the latest price, and simply work off the previously published price.

  • settlement_price trades away responsiveness for accuracy.

    • settlement_price is based on TWAP price over 15 minutes before the expiration time 8am UTC of each exchange.

    • There may be up to several seconds of delay for settlement_price to come through.

    • But it is guaranteed to be always highly precise and accurate.

settlement_price always TWAPs over spot_prices, since all options and futures are settled based on spot_price.

Mark Price

Mark Prices are computed using the below formula:

MarkPrice=TheoreticalPrice+(PreTradeEwma+PostTradeEwma)/2MarkPrice = TheoreticalPrice + (PreTradeEwma + PostTradeEwma) / 2

This equation introduces three new concepts. Ignore theoretical_price for now, simply assume that there exists a fair, accurate, and responsive theoretical_price for each and every derivative contract traded on GRVT. We will get to it in a later section. We will first focus on the EWMA components.

Note that all the computations shared in this section are performed by a third-party oracle, and signed by the oracle’s private key. GRVT has no way to manipulate the mark prices on our smart contracts.

Mark Price Adjustments

The purpose of the pre_trade_ewma and post_trade_ewma components are to adjust the theoretical_price such that we yield a mark_price that is fine-tuned towards both the pre-trade mark_price and the post-trade last_price that are occurring on our exchange. Variables such as the settlement currency, margin model, and liquidity would cause the theoretical_price (that is aggregated from various exchanges) to diverge slightly from the trading activity on the GRVT order book. These mark price adjustments help to account for those differences, and yield a mark price that is calibrated towards the GRVT order book.

Take note that:

  • GRVT’s EWMA components track price differences between

    • mid_price and theoretical_price

    • last_price and theoretical_price

  • Price is a fast-moving metric, whereas price difference is a slow-moving metric.

    • i.e. If a perpetual on our exchange consistently trades $5 above theoretical_price, likely, this price differential will not fluctuate wildly from moment to moment.

  • EWMA is a lagging/stable indicator, and is generally not highly responsive.

    • It is more desirable to apply it towards slow-moving metrics than towards fast-moving metrics.

  • EWMA, when used to track price differences, is resilient against adverse conditions

    • If there are no quotes in the order book, pre_trade_ewma simply does not update.

    • If there is no trading activity, post_trade_ewma simply does not update.

    • The price differences continue to be stable, and accurate.

    • This quality of EWMA makes it more suitable for tracking price differences on naturally illiquid instruments (options) compared to time-bound indicators such as 5-minute moving averages.

  • Given the assumption that the theoretical_price is fair, accurate, and responsive

    • Using EWMA to track price differences always yields responsive prices that are well adjusted towards GRVT’s order book.

EWMA

EWMA (Exponentially Weighted Moving Average) is a lagging/stable indicator that applies more weight towards recent values, and less weight towards less recent values. It is a lagging indicator that is appropriate for placing more bias towards more recent values.

A standard EWMA formula is as follows:

EWMAt=α×rt+(1−α)×EWMAt−1EWMA_t = \alpha \times r_t + (1 - \alpha) \times EWMA_{t-1}

Alpha: α\alpha

  • α \alpha is a weight

  • The higher the α \alpha , the more the EWMA adjusts to recent prices.

Value: rt r_t

  • rt r_t is the value that we are tracking.

  • rt r_t = (last_traded_price OR book_mid_price) - theoretical_price

Pre-Trade EWMA

PreTradeEwmat=α×rt+(1−α)×PreTradeEwmat−1PreTradeEwma_t = \alpha \times r_t + (1 - \alpha) \times PreTradeEwma_{t-1}

Where

  • α \alpha = 0.002

  • rt r _t = (mid_price - theoretical_price)

Rationale for α \alpha = 0.002:

  • GRVT publishes tickers every 100ms

  • Over a 1 second period, there are 10 ticker updates

    • The last 1 second of values will make up 2% of the EWMA ( 1-(0.998)^10 )

  • Over a 1 minute period, there are 600 ticker updates

    • The last 1 minute of values will make up 70% of the EWMA ( 1-(0.998)^600 )

  • Over a 5-minute period, there are 3000 ticker updates

    • The last 5 minutes of values will make up 99.8% of the EWMA ( 1-(0.998)^3000 )

  • When the order book is empty, mid_price will take on a null value, and the EWMA is not updated.

Post-Trade EWMA

PostTradeEwmat=α×rt+(1−α)×PostTradeEwmat−1PostTradeEwma_t = \alpha \times r_t + (1 - \alpha) \times PostTradeEwma_{t-1}

Where

  • α \alpha = config_weight * min(last_notional/config_notional, 1)

  • config_weight = 0.1

  • config_notional = $1000

  • rt r _t = (last_price - index_price)

Rationale for config_weight = 0.1:

  • The largest amount a single large trade can affect our EWMA is by 0.1

    • This limits the impact of large trades on our EWMA

  • The last 10 trades will maximally make up 65% of the EWMA ( 1-(0.9)^10 )

  • The last 20 trades will maximally make up 88% of the EWMA ( 1-(0.9)^20 )

  • The last 50 trades will maximally make up 99.5% of the EWMA ( 1-(0.9)^50 )

  • When there is no trading activity, the EWMA is not updated.

Rationale for config_notional = $1000:

  • We do not want multiple small trades to affect our EWMA too much

  • Trades that are lower than config_notional will have linearly less impact on EWMA.

    • A trade of $500 will only make up 5% of the EWMA

    • A trade of $200 will only make up 2% of the EWMA

Theoretical Price

The above mark price adjustments are only useful when applied onto a fair, accurate, and responsive theoretical_price. GRVT will leverage the following methodologies to compute theoretical prices for all derivative contracts traded on our exchange.

Perpetuals

The theoretical_price for perpetuals is simply its index_price. Given the high liquidity and trading volume of perpetual contracts, GRVT is able to retrieve a fair, accurate, and responsive theoretical_price with relative ease.

All perpetual mark_prices are delivered at 200ms frequency on our Market Data endpoints.

Futures

While GRVT can simply adopt the same heuristic for futures, it would limit GRVT’s long-term ability to provide custom-dated futures that are not traded on other exchanges. Instead, GRVT uses a forward_price as the theoretical_price.

See: Forward Price: Definition, Formulas for Calculation, and Example

The index_prices of future contracts are reverse-engineered into a risk-free rate curve. This risk-free rate curve is then applied on the index_price of the underlying asset to yield a forward_price.

This forward_price will almost always be identical to the futures index_price given that they are computed from the same source. It is, however, free from risk-free rate arbitrage, and may differ from time to time when such arbitrage opportunities exist. It also has the benefit of providing 100% uptime. Even in the event that an illiquid futures order book goes dark, the forward_price continues to be up. The risk-free rate curve is smoothed over time using EWMA as well.

All futures mark_prices are delivered at 200ms frequency on our Market Data endpoints.

The risk-free rate curve is re-calibrated every 20s, but not a huge issue given that it is a slow-moving metric.

forward_prices are always highly responsive to spot price movements.

Options

Relying on the options index_price directly is typically a bad idea. Given that:

  • Options order books typically have large spreads

  • Options prices are typically highly volatile

  • Options order books are very frequently lacking any liquidity whatsoever

    • This is especially true for deep ITM/OTM options or options with longer term

As such, GRVT derives an option’s theoretical_price using the Black-Scholes model and uses three market indicators as input:

  • spot price

  • risk-free rate

  • implied volatility

The first two indicators have already been explained in the futures section. So let’s skip that and only focus on implied volatility.

Firstly, note that options price is a fast-moving metric and is not very suitable to be smoothed across time. However, implied volatility is a slow-moving metric and can benefit from time-based smoothing without serious loss of accuracy or responsiveness. This makes implied volatility much safer to rely on for options theoretical_price given the frequent outages of options order books.

GRVT’s IV Surface is built as follows:

  • Options index_prices are collected

  • ITM options prices are removed from consideration given their large spreads and low liquidity

    • This is safe to conduct given the call-put parity equation

    • The OTM prices on the other side can be used as a more reliable substitute

  • SVI parameters for the IV surface are then derived from the OTM options prices

    • This surface “fills in the gap” whenever specific mid_prices are missing from the order book

  • The IV surface is smoothed over time using EWMA

    • This yields a high-uptime IV surface that is resilient against order book outages

    • This also yields an arbitrage-free IV surface that is highly suitable for theoretical_price

This IV surface is re-calibrated every 20s similar to the situation with risk-free rate curves.

Lastly, by combining

  • A spot index_price that is naturally fair, accurate, and responsive

  • A risk-free rate that is smoothed over time, and is a slow-moving metric

  • An implied volatility that is smoothed over time, and is a slow-moving metric

GRVT is able to yield a fair, accurate, and responsive options theoretical_price that has 100% uptime.

All options mark_prices are delivered at 500ms frequency on our Market Data endpoints.

The IV surface is re-calibrated every 20s, but not a huge issue given that it is a slow-moving metric.

Options theoretical_prices are always highly responsive to spot price movements.

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